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** and Burnside's
** Burnside's problem, about the sizes of finite group mathematics
** Burnside's theorem, a theorem of group theory

** and lemma
** Zorn's lemma: Every non-empty partially ordered set in which every chain ( i. e. totally ordered subset ) has an upper bound contains at least one maximal element.
** Tukey's lemma: Every non-empty collection of finite character has a maximal element with respect to inclusion.
** word, lexeme, lemma, lexicon, vocabulary, terminology
** Noether normalization lemma
** Schwarz – Ahlfors – Pick theorem, an extension of the Schwarz lemma for hyperbolic manifolds
** Sperner's lemma
** Schwarz lemma
** The Lovász local lemma ( proved in 1975, by László Lovász & P. Erdős )
** Algorithmic Lovász local lemma ( proved in 2009, by Robin Moser and Gábor Tardos )
** Krasner's lemma, in number theory
** Hensel's lemma and Henselian rings, named after Kurt

** and theorem
** Well-ordering theorem: Every set can be well-ordered.
** Tarski's theorem: For every infinite set A, there is a bijective map between the sets A and A × A.
** König's theorem: Colloquially, the sum of a sequence of cardinals is strictly less than the product of a sequence of larger cardinals.
** Tychonoff's theorem stating that every product of compact topological spaces is compact.
** If S is a set of sentences of first-order logic and B is a consistent subset of S, then B is included in a set that is maximal among consistent subsets of S. The special case where S is the set of all first-order sentences in a given signature is weaker, equivalent to the Boolean prime ideal theorem ; see the section " Weaker forms " below.
** The Vitali theorem on the existence of non-measurable sets which states that there is a subset of the real numbers that is not Lebesgue measurable.
** Stone's representation theorem for Boolean algebras needs the Boolean prime ideal theorem.
** The Nielsen – Schreier theorem, that every subgroup of a free group is free.
** The Hahn – Banach theorem in functional analysis, allowing the extension of linear functionals
** The theorem that every Hilbert space has an orthonormal basis.
** The Banach – Alaoglu theorem about compactness of sets of functionals.
** The Baire category theorem about complete metric spaces, and its consequences, such as the open mapping theorem and the closed graph theorem.
** Gödel's completeness theorem for first-order logic: every consistent set of first-order sentences has a completion.
** The numbers and are not algebraic numbers ( see the Lindemann – Weierstrass theorem ); hence they are transcendental.
** Hilbert's basis theorem
** Bayes ' theorem
** More generally, Rademacher's theorem extends the differentiability result to Lipschitz mappings between Euclidean spaces: a Lipschitz map ƒ: U → R < sup > m </ sup >, where U is an open set in R < sup > n </ sup >, is almost everywhere differentiable.
** Lyapunov's central limit theorem
** Superposition theorem, in electronics
** " Kelvin's vorticity theorem for incompressible or barotropic flow ".
** Artin reciprocity law, a general theorem in number theory that provided a partial solution to Hilbert's ninth problem
** Various proofs of the four colour theorem.

** and group
** For every non-empty set S there is a binary operation defined on S that makes it a group.
** In topology, morphisms between topological spaces are called continuous maps, and an automorphism of a topological space is a homeomorphism of the space to itself, or self-homeomorphism ( see homeomorphism group ).
** Terminology of the British Isles, discusses the sometimes ambiguous or contentious names for parts of the island group
** The B-52's ( album ), an album by the eponymous group
** School band, a group of student musicians who rehearse and perform instrumental music together
** Marching band, a group of performers that consist of instrumental musicians who generally perform outdoors and incorporate some type of marching ( and possibly other movements ) with their musical performance
** Han Chinese, the dominant ethnic group in mainland China, Taiwan and Singapore
** the exceptional and twisted groups of Lie type ( including the Tits group ).
** Religion and blood group with RH factor
** Religion ( or " NRE " if none ) and blood group with RH factor
** Blood group with RH factor
** First and middle initials and suffix ; blood group
** Social Security number with no dashes or spaces followed immediately by " USN ", space, blood group
** Blood group
** Fermentative hydrogen production, the fermentative conversion of organic substrate to biohydrogen manifested by a diverse group of bacteria
** The Pferdestärke PS ( German translation of horsepower ) is a name for a group of similar power measurements used in Germany around the end of the 19th century, all of about one metric horsepower in size.
** Propithecus diadema group
** Propithecus verreauxi group
** Parabolic induction: a method of constructing group representations of a reductive group from representations of its parabolic subgroups.
** five lectures, heard by the group, as blip. tv videos
** Diagnosis-related group
** Kuru ( archaeology ), an Indo-Aryan ethnic group
** Order † Sparassodonta ( formerly viewed as marsupials, now as a sister group of metatherians )

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